Mathematics, 10.12.2019 11:31 chriscol4082

Jim and stephanie just got married and are thinking about changing their health care insurance plans to be more affordable. currently, both jim and stephanie are insured through their own employers. jim’s employer pays 42% of his $378 monthly premium. his insurance plan will also pay for 23% of the $345 premium for additional beneficiaries. stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary stephanie adds to her plan. her employer would then pay 30% of the $349 premium for each additional beneficiary.

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Answer from: GgRed

Stephanie’s plan is more affordable than Jim.

Further explanation:

Step by step explanation:

Step 1:

It is given that Jim’s employer paid $42\%$ of his $\$ 378$ monthly premium.

Therefore the rest of the percent is given by Jim.

Now find the rest of percent of the premium that is given by Jim.

$100\% - 42\% = 58\%$

The amount paid by Jim for his premium can be calculated as,

$\begin{aligned}{\text{amount paid by Jim}}&= 58\% {\text{ of }}378\\&= \frac{{58}}{{100}} \times 378\\&= 219.24\\\end{aligned}$

Step 2:

Now it is given that Jim’s insurance plan pays additional beneficiaries that is $23\%$ of $\$ 345$ premium.

Therefore the rest of the percent is given by Jim.

Now find the rest of percent of the additional premium that is given by Jim.

$100\% - 23\% = 77\%$

The amount paid by Jim for his additional premium can be calculated as,

$\begin{aligned}{\text{amount paid by Jim}} &= 77\% {\text{ of }}350\\&=\frac{{77}}{{100}} \times 350\\ &= 265.65\\\end{aligned}$

Now calculate the total premium paid by Jim as,

$\begin{aligned}{\text{total amount paid}} &= \$ 219.24 + \$ 265.65\\&= \$ 484.89\\\end{aligned}$

Step 3

It is given that Stephanie’s employer paid $35\%$ of his $\$ 298$ monthly premium and offers extra $10\%$ of his premium

Therefore the rest of the percent is given by Stephanie.

Now find the rest of percent of the premium that is given by Stephanie.

$100\% - 35\% - 10\% = 55\%$

The amount paid by Jim for his premium can be calculated as,

$\begin{aligned}{\text{amount paid by Jim}} &= 55\% {\text{ of 29}}8\\&= \frac{{55}}{{100}} \times 298\\&= 163.90\\\end{aligned}$

Step 4:

Now it is given that Stephanie’s insurance plan pays additional beneficiaries that is $30\%$ of $\$ 349$ premium.

Therefore, the rest of the percent is given by Jim.

Now find the rest of percent of the additional premium that is given by Stephanie.

$100\% - 30\% = 70\%$

The amount paid by Stephanie for his additional premium can be calculated as,

$\begin{aligned}{\text{amount paid by Jim}} &= 70\% {\text{ of }}349\\&= \frac{{70}}{{100}} \times 349\\&= 244.30\\\end{aligned}$

Now calculate the total premium paid by Stephanie as,

$\begin{aligned}{\text{total amount paid}} &= \$ 163.90 + \$ 224.30\\&= \$ 408.20\\\end{aligned}$

Step 5:

From step 2, the amount paid by Jim is $\$ 484.89$ and from step 4 the amount paid by Stephanie is $\$ 408.20$ .

It can be seen that Stephanie is paying less than Jim.

Therefore Stephanie should add Jim to her plan as Stephanie’s plan is more affordable than Jim.

Learn more:

Learn more about the solution of the linear equation Learn more about the problem of the linear equation Learn more about midpoint of the segment

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Percentage

Keywords: Jim, Stephanie, Percentage, premium, insurance plan, beneficiaries, amount, paid, employer, paid, additional, division, multiplication, number

Answer from: Quest

step-by-step explanation:

Answer from: Quest

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